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Naseer Shahzad - One of the best experts on this subject based on the ideXlab platform.
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Convergence to a Common Fixed Point of a Finite Family of Generalized Asymptotically Nonexpansive Mappings
Bulletin of the Malaysian Mathematical Sciences Society, 2015Co-Authors: Habtu Zegeye, Naseer Shahzad, Onkabetse A. DamanAbstract:We introduce an iterative process which converges strongly to a common fixed point of a Finite Family of uniformly continuous generalized asymptotically nonexpansive mappings in Hilbert spaces. As a consequence, results on convergence to a common fixed point of a Finite Family of uniformly continuous asymptotically nonexpansive in the intermediate sense and asymptotically nonexpansive mappings are proved.
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Convergence theorem for common fixed points of a Finite Family of multi-valued Bregman relatively nonexpansive mappings
Fixed Point Theory and Applications, 2014Co-Authors: Naseer Shahzad, Habtu ZegeyeAbstract:In this paper, it is our purpose to introduce an iterative process for the approximation of a common fixed point of a Finite Family of multi-valued Bregman relatively nonexpansive mappings. We prove that the sequence of iterates generated converges strongly to a common fixed point of a Finite Family of multi-valued Bregman nonexpansive mappings in reflexive real Banach spaces. MSC:47H05, 47H09, 47H10, 47J25, 49J40, 90C25.
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Approximation of the common minimum-norm fixed point of a Finite Family of asymptotically nonexpansive mappings
Fixed Point Theory and Applications, 2013Co-Authors: Habtu Zegeye, Naseer ShahzadAbstract:We introduce an iterative process which converges strongly to the common minimum-norm fixed point of a Finite Family of asymptotically nonexpansive mappings. As a consequence, convergence result to a common minimum-norm fixed point of a Finite Family of nonexpansive mappings is proved.
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Strong convergence theorems for a Finite Family of nonexpansive mappings and semigroups via the hybrid method
Nonlinear Analysis: Theory Methods & Applications, 2010Co-Authors: Habtu Zegeye, Naseer ShahzadAbstract:Strong convergence theorems are obtained for a Finite Family of nonexpansive mappings and semigroups by the hybrid method. © 2009 Elsevier Ltd. All rights reserved.
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best proximity sets and equilibrium pairs for a Finite Family of multimaps
Fixed Point Theory and Applications, 2008Co-Authors: M A Althagafi, Naseer ShahzadAbstract:We establish the existence of a best proximity pair for which the best proximity set is nonempty for a Finite Family of multimaps whose product is either an -multimap or a multimap such that both and are closed and have the KKM property for each Kakutani multimap . As applications, we obtain existence theorems of equilibrium pairs for free 1-person games as well as for free 1-person games. Our results extend and improve several well-known and recent results.
Habtu Zegeye - One of the best experts on this subject based on the ideXlab platform.
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Approximating a common fixed point of a Finite Family of nonlinear mappings in modular function spaces
Computational and Applied Mathematics, 2019Co-Authors: Getahun Bekele Wega, Habtu ZegeyeAbstract:In this study, it is our purpose to investigate an algorithm for approximating a common fixed point of a Finite Family of \(\rho \)-quasi-nonexpansive mappings. In addition, we propose and analyze a scheme which estimates a common fixed point of a Finite Family of multivalued mappings in modular function spaces. As a consequence, we establish the \(\rho \)-convergence of the proposed algorithms under some mild conditions. In addition, some numerical examples which support our main results are presented. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.
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An algorithm for approximating a common fixed point of a Finite Family of Lipschitz pseudocontractive multi-valued mappings
Advances in Fixed Point Theory, 2016Co-Authors: Sebsibe Teferi Woldeamanuel, Mengistu Goa Sangago, Habtu ZegeyeAbstract:The purpose of this paper is twofold. We first give erratum to a proof given by Woldeamanuel et al. [Strong convergence theorems for a common fixed point of a Finite Family of Lipschitz hemicontractive-type multivaled mappings, Adv. Fixed Point Theory, 5 (2015), No. 2, 228-253]. In addition, we study an algorithm which approximates a common fixed point of a Finite Family of Lipschitz pseudocontractive multi-valued mappings under appropriate conditions.
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Convergence to a Common Fixed Point of a Finite Family of Generalized Asymptotically Nonexpansive Mappings
Bulletin of the Malaysian Mathematical Sciences Society, 2015Co-Authors: Habtu Zegeye, Naseer Shahzad, Onkabetse A. DamanAbstract:We introduce an iterative process which converges strongly to a common fixed point of a Finite Family of uniformly continuous generalized asymptotically nonexpansive mappings in Hilbert spaces. As a consequence, results on convergence to a common fixed point of a Finite Family of uniformly continuous asymptotically nonexpansive in the intermediate sense and asymptotically nonexpansive mappings are proved.
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Convergence theorem for common fixed points of a Finite Family of multi-valued Bregman relatively nonexpansive mappings
Fixed Point Theory and Applications, 2014Co-Authors: Naseer Shahzad, Habtu ZegeyeAbstract:In this paper, it is our purpose to introduce an iterative process for the approximation of a common fixed point of a Finite Family of multi-valued Bregman relatively nonexpansive mappings. We prove that the sequence of iterates generated converges strongly to a common fixed point of a Finite Family of multi-valued Bregman nonexpansive mappings in reflexive real Banach spaces. MSC:47H05, 47H09, 47H10, 47J25, 49J40, 90C25.
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Approximation of the common minimum-norm fixed point of a Finite Family of asymptotically nonexpansive mappings
Fixed Point Theory and Applications, 2013Co-Authors: Habtu Zegeye, Naseer ShahzadAbstract:We introduce an iterative process which converges strongly to the common minimum-norm fixed point of a Finite Family of asymptotically nonexpansive mappings. As a consequence, convergence result to a common minimum-norm fixed point of a Finite Family of nonexpansive mappings is proved.
Suthep Suantai - One of the best experts on this subject based on the ideXlab platform.
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Monotone Hybrid Methods for a Finite Family of Nonexpasive Multi-valued Maps and Equilibrium Problems
Advances in systems science and applications, 2011Co-Authors: Suthep Suantai, Watcharaporn CholamjiakAbstract:In this paper, we introduce a new monotone hybrid iterative scheme for finding a common element of the set of common fixed points of a Finite Family of nonexpansive multivalued maps and the set of the solutions of the equilibrium problem in a Hilbert space. Moreover,we also introduce a new iterative scheme for finding a common fixed point of a Finite Family of nonexpansive multi-valued maps in a Banach space. Strong convergence theorem of the proposed iteration is established.
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a new mapping for finding common solutions of equilibrium problems and fixed point problems of Finite Family of nonexpansive mappings
Nonlinear Analysis-theory Methods & Applications, 2009Co-Authors: Atid Kangtunyakarn, Suthep SuantaiAbstract:Abstract In this paper, we introduce and study a new mapping generated by a Finite Family of nonexpansive mappings and Finite real numbers and introduce a general iterative method concerning the new mappings for finding a common element of the set of solutions of an equilibrium problem and of the set of common fixed points of a Finite Family of nonexpansive mappings in a Hilbert space. Then, we prove a strong convergence theorem of the proposed iterative method for a Finite Family of nonexpansive mappings to the unique solution of variational inequality which is the optimality condition for a minimization problem. Our main result can be applied to obtain strong convergence of the general iterative methods which are modifications of those in [G. Marino, H.K. Xu, A general iterative method for nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl. 318 (1) (2006) 43–52; S. Plubtieng, R. Punpaeng, A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 336 (1) (2007) 455–469; S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (1) (2007) 506–515] to a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping.
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hybrid iterative scheme for generalized equilibrium problems and fixed point problems of Finite Family of nonexpansive mappings
Nonlinear Analysis: Hybrid Systems, 2009Co-Authors: Atid Kangtunyakarn, Suthep SuantaiAbstract:Abstract In this paper, we introduce a new mapping and a Hybrid iterative scheme for finding a common element of the set of solutions of a generalized equilibrium problem and the set of common fixed points of a Finite Family of nonexpansive mappings in a Hilbert space. Then, we prove the strong convergence of the proposed iterative algorithm to a common fixed point of a Finite Family of nonexpansive mappings which is a solution of the generalized equilibrium problem. The results obtained in this paper extend the recent ones of Takahashi and Takahashi [S. Takahashi, W. Takahashi, Strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a Hilbert space, Nonlinear Anal. 69 (2008) 1025–1033].
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A New Iterative Method for Common Fixed Points of a Finite Family of Nonexpansive Mappings
International Journal of Mathematics and Mathematical Sciences, 2009Co-Authors: Suwicha Imnang, Suthep SuantaiAbstract:Let be a real uniformly convex Banach space and a closed convex nonempty subset of . Let be a Finite Family of nonexpansive self-mappings of . For a given , let and , , be sequences defined , where for all , and . In this paper, weak and strong convergence theorems of the sequence to a common fixed point of a Finite Family of nonexpansive mappings are established under some certain control conditions.
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A New Hybrid Algorithm for Variational Inclusions, Generalized Equilibrium Problems, and a Finite Family of Quasi-Nonexpansive Mappings
Fixed Point Theory and Applications, 2009Co-Authors: Prasit Cholamjiak, Suthep SuantaiAbstract:We proposed in this paper a new iterative scheme for finding common elements of the set of fixed points of a Finite Family of quasi-nonexpansive mappings, the set of solutions of variational inclusion, and the set of solutions of generalized equilibrium problems. Some strong convergence results were derived by using the concept of -mappings for a Finite Family of quasi-nonexpansive mappings. Strong convergence results are derived under suitable conditions in Hilbert spaces.
Xiaolong Qin - One of the best experts on this subject based on the ideXlab platform.
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Convergence Theorems of Fixed Points for a Finite Family of Nonexpansive Mappings in Banach Spaces
Fixed Point Theory and Applications, 2008Co-Authors: Yeol Je Cho, Shin Min Kang, Xiaolong QinAbstract:We modify the normal Mann iterative process to have strong convergence for a Finite Family nonexpansive mappings in the framework of Banach spaces without any commutative assumption. Our results improve the results announced by many others.
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Strong Convergence Theorems for a Finite Family of Nonexpansive Mappings
Fixed Point Theory and Applications, 2007Co-Authors: Meijuan Shang, Xiaolong QinAbstract:We modified the classic Mann iterative process to have strong convergence theorem for a Finite Family of nonexpansive mappings in the framework of Hilbert spaces. Our results improve and extend the results announced by many others.
Jin-ping Wang - One of the best experts on this subject based on the ideXlab platform.
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Strong Convergence of a New Iteration for a Finite Family of Accretive Operators
Fixed Point Theory and Applications, 2009Co-Authors: Jin-ping WangAbstract:The viscosity approximation methods are employed to establish strong convergence of the modified Mann iteration scheme to a common zero of a Finite Family of accretive operators on a strictly convex Banach space with uniformly Gâteaux differentiable norm. Our work improves and extends various results existing in the current literature.